Final answer:
Scientific notation expresses numbers as a product of a coefficient and a power of 10, simplifying arithmetic operations, especially for very large or very small numbers. For addition and subtraction, the same power of 10 is needed, while multiplication and division allow for different powers of 10.
Step-by-step explanation:
Numbers in scientific notation are written as a product of a coefficient (between 1 and 10) and a power of 10. For example, the number 79,345 in scientific notation is 7.9345 × 10⁴. Non-examples of scientific notation are standard numbers like 500 or 0.003, which have not been converted to the format of a coefficient multiplied by a power of 10.
When adding or subtracting numbers in scientific notation, the power of 10 must be the same because you are working within the same order of magnitude and only the coefficients are being directly added or subtracted. Different powers of 10 would imply different orders of magnitude, which cannot be combined without first adjusting them to a common power of 10.
In multiplication and division of numbers in scientific notation, the powers of 10 can differ because you are manipulating the order of magnitude through the respective operations. When multiplying, you add the exponents; when dividing, you subtract the exponents from each other. For instance, (3 × 10⁵) × (2 × 10°) = 6 × 10⁵, as the coefficients are multiplied and the exponents are added.